Note of caution; understand your foreclosure laws, depending on where this is in the process, attempting to pull investor ploys without having the ability to purchase yourself as implied under the contract can land you up against federal law, a lender can clean your clock for interference with an insured depository.In other words, investors who lack the ability and intent to buy themselves as stated in a contract with someone in foreclosure should stay clear of any attempt of trying to pull off anything except a true a cash sale.   

I read David Greene's SOLD book and want to apply his principles.Any other tips or advice?  

Change the locks, clean it up, and get it rented.

Otherwise you will find yourself in the clean/replace cycle.  

My issue is this: I need my place back so I can clean it up and make it look presentable for the appraiser because I want to cash out refi.

Have your sewers cleaned every other year for peace of mind...cheap insurance!

If you leave the property by the lease expiration date AND leave the property clean and in as good condition as you found it I will not charge rent for Jan. and I will return the security deposit in full" I made the offer contingent on them responding to my message. 

@Amanda SchneiderThey need to repair it or make concessions.You went under contract with a basement in good condition and that's no longer the case.It's nobodies fault, but the condition changed in a significant way before you closed.I would try to negotiate a concession for the issue in exchange for keeping the same closing date, just get it cleaned up asap and the repairs done after closing.Just make sure to give yourself some wiggle room in the concession amount because of the increased risk your taking on.

This could mean an extra electric bill for you and/or cleaning.- Fire monitoring. 

The fact that you cleaned everything up after the 10 days' notice and nothing had changed during that time, she hadn't paid the rent AND all of the furniture had been moved out, I would have done the same as you.